Understanding 3/9 As A Decimal: Conversion, Representation, And Simplification

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Learn how to convert 3/9 to a decimal, find its decimal representation, simplify it to lowest terms, and express it as a percentage. Understand the concept of 3/9 as a decimal.

Understanding 3/9 as a Decimal

What is 3/9?

When we talk about 3/9, we are referring to a fraction. Specifically, it means that we have 3 parts out of a total of 9 equal parts. Fractions are a way to represent numbers that are not whole numbers or decimals. In this case, 3/9 represents a fraction where the numerator (the top number) is 3, and the denominator (the bottom number) is 9.

Converting 3/9 to a Decimal

To convert 3/9 to a decimal, we divide the numerator by the denominator. In this case, we divide 3 by 9. When we perform the division, we get the decimal representation of the fraction. Let’s do the division:

3 ÷ 9 = 0.333333333...

The decimal form of 3/9 is approximately 0.333333333…, where the 3’s continue indefinitely. This is called a repeating decimal because the digit 3 repeats infinitely.

Decimal Representation of 3/9

As mentioned earlier, the decimal representation of 3/9 is approximately 0.333333333…. However, it’s important to note that this decimal is not exact. The 3’s after the decimal point continue infinitely, without ever reaching a final value. This is because the fraction 3/9 cannot be expressed as a terminating decimal, where the numbers after the decimal point eventually end.

Simplifying 3/9 to Lowest Terms

When simplifying a fraction, we aim to express it in its lowest terms. This means that the numerator and denominator have no common factors other than 1. To simplify 3/9, we can divide both the numerator and denominator by their greatest common factor, which is 3. Let’s simplify:

3/9 ÷ 3/3 = 1/3

So, the fraction 3/9 simplifies to 1/3. This means that 1 part out of 3 equal parts is equivalent to the original fraction of 3/9.

Equivalent Decimal for 3/9

The equivalent decimal for 3/9 is 0.333333333…. We obtained this by dividing 3 by 9 as mentioned earlier. This decimal, as we discussed, is a repeating decimal where the digit 3 repeats infinitely.

Expressing 3/9 as a Percentage

To express 3/9 as a percentage, we multiply the decimal representation (0.333333333…) by 100. Let’s do the calculation:

0.333333333... × 100 = 33.333333333...

So, when we express 3/9 as a percentage, it is approximately equal to 33.33%.

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